The star formation rate cookbook at 1 < z < 3: Extinction-corrected relations for UV and [OII]λ3727 luminosities

Aims: In this paper we use a well-controlled spectroscopic sample of galaxies at 1 <z< 3 drawn from the Galaxy Mass Assembly ultra-deep Spectroscopic Survey (GMASS) to study different star formation rate (SFR) estimators. In particular, we use infrared (IR) data to derive empirical calibrations to correct ultraviolet (UV) and [OII]λ3727 luminosities for dust extinction and dust-corrected estimates of SFR. Methods: We selected 286 star-forming galaxies with spectroscopic redshift 1 <z< 3. In order to have a homogeneous wavelength coverage in the spectra, the sample was divided into two sub-groups: galaxies at 1 <z< 1.6 whose spectra cover the rest-frame range ~2700-4300 Å, where the [OII]λ3727 emission line can be observed, and galaxies at 1.6 <z< 3 whose spectra cover the range ~1100-2800 Å. In the selection procedure we fully exploit the available spectroscopic information. In particular, on the basis of three continuum indices, we are able to identify and exclude from the sample galaxies in which old stellar populations might bring a non-negligible contribution to IR luminosity (LIR) and continuum reddening. Using Spitzer-MIPS and Herschel-PACS data we derive LIR for two-thirds of our sample. The LIR/LUV ratio is used as a probe of effective attenuation (AIRX) to search for correlations with continuum and spectroscopic features in order to derive empirical calibrations to correct UV and [OII]λ3727 luminosities for dust extinction. Results: Through the analyses of the correlations between different dust attenuation probes, a set of relations is provided that allows the recovery of the total unattenuated SFR for star-forming galaxies at 1 <z< 3 using UV and [OII]λ3727 luminosities. The relation between AIRX and UV continuum slope (β) was tested for our sample and found to be broadly consistent with the literature results at the same redshift, though with a larger dispersion with respect to UV-selected samples. We find a correlation between the rest-frame equivalent width of the [OII]λ3727 line and β, which is the main result of this work. We therefore propose the rest-frame equivalent width of the [OII]λ3727 line as a dust attenuation probe and calibrate it through AIRX, though the assumption of a reddening curve is still needed to derive the actual attenuation towards the [OII]λ3727 line (A[OII]). We tested the issue of differential attenuation towards stellar continuum and nebular emission: our results are in line with the traditional prescription of extra attenuation towards nebular lines. Finally, we use our set of cross-calibrated SFR estimates to look at the relation between SFR and stellar mass. The galaxies in our sample show a close linear relation (σ = 0.3 dex) at all redshifts with a slope ~0.7-0.8, which confirms several previous results. Appendix A is available in electronic form at http://www.aanda.org